PSI - Issue 47

L.A. Almazova et al. / Procedia Structural Integrity 47 (2023) 417–425 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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3.3. Effect of the radius of the sphere In this Section, the influence of the radius of curvature of the pressure vessel on the pit growth is investigated, the thickness of the vessel and other parameters being the same. In particular, apart from the sphere of the radii addressed above, we consider sphere of the radii R=250 mm, r=240 mm and R=150 mm, r=140 mm. Calculations revealed that a decrease in the ratio of the middle radius of the vessel to its curvature results in reducing the maximum principal stress at the bottom of the pits. The growth rate of the pitting also decreases with decreasing radii of the vessel, due to mechanochemical effect. For example, table 2 shows calculation results for the case with h1=2 mm, h2=2 mm and D=2 mm for different sizes of the sphere. It is seen that the maximum principal stress decreases significantly with decreasing radii, at constant thickness. The growth rates of pits (which are linearly dependent on stresses) also decrease; the decrease in growth rate being dependent on the kinetics constant m .

Table 2. The dependence of the pits growth rate and the stress values at the pits’ bottom on the radii of the sphere

Propagation rate of the first pit at the initial moment, mm / 0,129

Propagation rate of the second pit at the initial moment, mm / 0,128

Stress at the bottom of the first pit, MPa

Stress at the bottom of the second pit, MPa

Sizes of the vessel, mm

R=350, r=340 R=250, r=240 R=150, r=140

36,29 25,16 14,54

35,73 25,13 14,67

0,120 0,111

0,120 0,111

3.4. Effect of the distance between the pits

In this Section we analyse the effect of the distance between the pits on the maximum stress and the pit growth rate, other parameter being equal. It was observed that for considered geometrical parameters, the maximum principal stress at the bottom of pits slightly decreases with the increasing distance, thus slightly decreasing the pit growth rate. For example, for the sphere with R=250 mm and r=240 mm the maximum stresses decreased by about 1MPa with the increase in D from 4 mm to 8 mm. However, it should be noted that changing D leads to a change in the stress distribution in the vicinity of defects. In some cases, maximum stresses are observed at the edges of the defects, in the ligament between the pits (Figure 1b). In other situations, maximum stresses are at the bottom of the defects (Figure 1a). For example, in the sphere of the radii R=250 mm, r=240 mm or R = 150 mm, r = 140 mm, at D = 0.5 mm and D = 1 mm (except for the case of h1=2 mm, h2=2 mm), the maximum stresses are reached at the edges between the pits. With increasing distance, i.e., D = 2 mm and D=4 mm, the maximum is reached at the bottom of the pits. Hence, for relatively large values of D, pits do not influence each other, while as D decreases, the interaction between the pits begins to appear.